What are the divisors of 9064?

1, 2, 4, 8, 11, 22, 44, 88, 103, 206, 412, 824, 1133, 2266, 4532, 9064

There is a total of 16 positive divisors.
The sum of these divisors is 18720.
The arithmetic mean is 1170.

12 even divisors

2, 4, 8, 22, 44, 88, 206, 412, 824, 2266, 4532, 9064

4 odd divisors

1, 11, 103, 1133

How to compute the divisors of 9064?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9064 by each of the numbers from 1 to 9064 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9064 / 1 = 9064 (the remainder is 0, so 1 is a divisor of 9064)
9064 / 2 = 4532 (the remainder is 0, so 2 is a divisor of 9064)
9064 / 3 = 3021.3333333333 (the remainder is 1, so 3 is not a divisor of 9064)
...
9064 / 9063 = 1.0001103387399 (the remainder is 1, so 9063 is not a divisor of 9064)
9064 / 9064 = 1 (the remainder is 0, so 9064 is a divisor of 9064)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9064 (i.e. 95.205041883295). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9064 / 1 = 9064 (the remainder is 0, so 1 and 9064 are divisors of 9064)
9064 / 2 = 4532 (the remainder is 0, so 2 and 4532 are divisors of 9064)
9064 / 3 = 3021.3333333333 (the remainder is 1, so 3 is not a divisor of 9064)
...
9064 / 94 = 96.425531914894 (the remainder is 40, so 94 is not a divisor of 9064)
9064 / 95 = 95.410526315789 (the remainder is 39, so 95 is not a divisor of 9064)